~ sharp 15 ( #15 )

~ Lydian Dorian Dance ~

~ the discovery ~

~ needing 12 pitches twice to close the loop ~

~ evolving beyond the diatonic realm ~

~ forward motion through arpeggios ~

~ the augmented double octave ~

~ ouch ! ~

'theory 'correcting' our most ancient sequence of pitches to create the chromatically alternating, Lydian and Dorian arpeggio cycle through each of the 12 key centers ... '

In a nutshell. Turns out that there's a way to advance our 12 pitch, closed chromatic loop a bit, evolve the diatonic realm so to speak, move to a fourth dimension for musical creations even. And along the way, create a new emotional environment for explorations, improvisations and compositions.

We do this by 'correcting' our core diatonic arpeggio, built up from our most common diatonic, relative major / minor group of pitches, through a more symmetrical build of the alternating major and minor thirds, used to create our arpeggios. Compare the interval formulas. Example 2.

~ one simple swap and .... kaboom ! ~
major scale interval sequence
maj 3rd
min 3rd
maj 3rd
min 3rd
min 3rd
maj 3rd
min 3rd
# 15 symmetrical sequence
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd

Cool ? We 'fix' the two consecutive minor 3rd's in the diatonic grouping, swap a major for minor, so as to get a perfect alternating of major and minor 3rd's symmetry. That's all there is to this theory. There's a minor 'flipside' inverted relative if you'll allow, which just inverts the sequence to minor / major. And voila, the Lydian / Dorian weave to all points beyond tonal universe; into a different tonal gravity and a new artistic sense of aural predictability in our creations :)

All points in that this symmetrical arpeggio will continue to loop until all of the 12 Lydian and 12 Dorian modal centers have been visited.

What results is a rather remarkable architecture that retains nearly all of the original framework of our two part, modal basis of the Ionian / Aeolian, relative major / minor tonal centering. With #15, our paired central modes are the now ancient Lydian and Dorian groups, that we inherited from Pythagoras 2500 years or so ago. There's also a bit of a tritone interval shift as the Four / Seven tritone pairing in the major scale is replaced by #11, which when capped by #15, takes on a new coloring from its traditional role in V7. Cool huh ? And its theory mumbo jumbo goes just like this :)

Historical origins pour moi. The following discussion and theory ideas originated way back in '82', with hearing this arpeggio lick sounded as the closing lick for the jazz standard "Smoke Gets In Your Eyes", as performed on piano by Dr. Alan Frank. Here in 'C' major. Example 1.

wiki ~ "Smoke Gets In Your Eyes"
Interesting sound yes? Click it again. And man if that ain't a true blue colortone marvel Hollywood chord to close the line ta boot ! Here's a bass line story for #15 pitches, tonic One up on through to #15, a double octave plus a half step arpeggio. From the lower root pitch 'C.' Example 1a.
major arpeggio
1
3
5
7
9
#11
13
15
# 15 symmetrical sequence
C
E
G
B
D
F#
A
C#
Cool ? Sounds pretty much like two major 7th arpeggios sounded back to back are supposed to sound yes ? Hmmm ... two major 7th chords ... wonder if minor will be two minor 7th chords ? Aren't these chords both a 'chord type' too ? Example 1b.
minor arpeggio
1
3
5
7
9
#11
13
15
# 15 symmetrical sequence
A
C
E
G
B
D
F#
A

Yep. Minor 3rd major 3rd minor 3rd major 3rd ... a pure perfecto. Yet somehow, this time we ended up on the same pitch ... ? So one of our two strands has perfect closure and the other does not ? Yep. Major minor was 'C to C#.' Minor to major was 'A to A.' So minor is different than major ?

It is Amigo, and that's what somehow allows for the 'Lydian / Dorian 'weave' to work its magics. One group ends and its last pitch, becomes the first of the new group. And each new group swaps major to minor, or if we start minor, then minor to major. You're kidding ? Nope :)

Correcting the diatonic arpeggio / Lydian major. Examine the following chart for intervals of the diatonic major scale respelled into its arpeggio. Turns out there's two 'minor 3rds' in a row to get the pitches diatonically correct. In building the #15 arpeggio's, we 'fix' this 'two minor 3rd's' with a pure alternating of the major 3rd and minor 3rds, (a simple swap of the second minor 3rd with its next interval works the magic). Thus the idea of 'correcting' the diatonic sequence. Compare the intervals and letter names of interval this theory from the root pitch 'C.' Example 2.

major scale interval sequence
.
maj 3rd
min 3rd
maj 3rd
min 3rd
min 3rd
maj 3rd
min 3rd
C major arpeggio
C
E
G
B
D
F
A
C
# 15 symmetrical sequence
.
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd
C arpeggio #15
C
E
G
B
D
F #
A
C#

Fairly straightforward yes? How about permutating this to an interval sequence of minor 3rd / major 3rd?

Correcting the diatonic arpeggio / Dorian minor. In this next idea we follow the same build process as just above but are thinking diatonic minor. Using the same pitches, we're now in the relative minor of 'C' major, so building up from the root pitch 'A.' Now we'll swap around the last two intervals in the arpeggio. Ex. 3.

minor scale interval sequence
.
min 3rd
maj 3rd
min 3rd
maj 3rd
min 3rd
min 3rd
maj 3rd
A minor arpeggio
A
C
E
G
B
D
F
A
# 15 symmetrical sequence
.
min 3rd
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd
min 3rd
A Dorian arpeggio
A
C
E
G
B
D
F#
A

Cool? Are you already in the know that 'F#' in A minor implies, 'A' Dorian from the second scale degree of the parent scale of 'G' major ? Cool.

Interesting, even as we evolve to Dorian mode pitches, we attain the perfect closure of the loop. Of course if we continued along with this symmetrical sequence, our next pitch would be a up a major 3rd from 'A', so to a 'C#', so no longer in the A minor tonality.

This 'transition link' from minor to major, and vice versa, becomes the basis for the consistent looping and the architectural structure that the #15 system provides; that one modal grouping of the pitches 'steps' by either major or minor 3rd right into the next, creating an alternating pattern of a Lydian / Dorian / Lydian / Dorian or vice versa, weaving and dance of these ancient musical pitches and colors.

Closing the loop, and here's where it gets crazy. In this next idea, we run the above pitch sequences out in our alternating major 3rd / minor 3rd sequence and look to close the loop back to our starting point our sequence. The pitches are broken down into groups of eight, so same number as generally found in a full octave, closed scale loop. Remember though we're still only working with tertian arpeggios for now. Example 4.

C
E
G
B
D
F#
A
C#
C#
E
G#
B
D#
F#
A#
C#
Db
F
Ab
C
Eb
G
Bb
D
D
F
A
C
E
G
...
...

The loop is closed, the 12 twice. From our starting point of C E G, a 'C' major triad, to C E G again, in the fourth row etc. So by just counting each letter pitch once in the above tables, and no enharmonic pitches either, after 24 interval episodes of the major 3rd / minor 3rd sequence, we arrive back to our starting pitch for the same sequence of pitches to begin again. So we've perfectly closed our loop.

Arpeggios into scales. From this last group of arpeggios, let's evolve from eight pitches into seven pitch scales. Example 4a.

C
E
G
B
D
F#
A
C#

... as a closed loop can become C Lydian ...

C
D
E
F#
G
A
B
C

Next loop.

C#
E
G#
B
D#
F#
A#
C# / Db

... as a closed loop can become C# Dorian ...

C#
D#
E
F#
G#
A#
B
C#

Next loop with the C# now as Db.

Db
F
Ab
C
Eb
G
Bb
D

... as a closed loop can become Db Lydian ...

Db
Eb
F
G
Ab
Bb
C
Db

Next loop.

D
F
A
C
E
G
B
D

... as a closed loop can become D Dorian ...

D
E
F
G
A
B
C
D

... looks like the pitch letter names of D Dorian to me ... :)

Cool ? It is tricky no doubt. Not the most complex of the theory in this book, but pretty darn close :)

The pattern ~ Lydian / Dorian double helix. Looking at the way this forms up, we see that when we extend our Lydian group it evolves into Dorian. Then Dorian, when symmetrically continued becomes Lydian again, as we ascendingly cycle chromatically through key centers. The reverse of this is also perfect; ascending Dorian arpeggio pitches continued through the #15 symmetrical cycle will morph into Lydian, then Dorian in a similar cycle of key centers. Here's a couple of measures of this evolution followed by a shorthand chart for linking all of the 12 Lydian and Dorian centers. Example 5.

If this looks like an arpeggio blasting off to you ... cool me too. Add in some new time and super quickness and sky's the limit :) Here's the double twist. Example 5a.

wiki ~ sheets of sound
C Lydian evolves into C# Dorian
C# Dorian evolves into Db Lydian
Db Lydian evolves into D Dorian
D Dorian evolves into D Lydian
D Lydian evolves into Eb Dorian
Eb Dorian evolves into Eb Lydian
Eb Lydian evolves into E Dorian
E Dorian evolves into E Lydian
E Lydian evolves into F Dorian
F Dorian evolves into Gb Lydian
Gb Lydian evolves into G Dorian
G Dorian evolves into G Lydian
G Lydian evolves into Ab Dorian
Ab Dorian evolves into Ab Lydian
Ab Lydian evolves into A Dorian
A Dorian evolves into A Lydian
A Lydian evolves into Bb Dorian
Bb Dorian evolves into Bb Lydian
Bb Lydian evolves into B Dorian
B Dorian evolves into B Lydian
B Lydian evolves into C Dorian
C Dorian evolves into C Lydian
... and our loop closes, so right back to where we started :)

Or vice versa. The flip side of this is also true; Dorian to Lydian creates a minor to major, perfectly sequential pattern of key centers too.

Spell out the pitches. In this next charting we simply spell out the sequencing of the letter name pitches for each of the entries in the above chart, by alternating our two intervals patterns; first major 3rd / minor 3rd then the minor 3rd / major 3rd pattern. Example 6.

maj / min
C
E
G
B
D
F#
A
C#
min / maj
C#
E
G#
B
D#
F#
A#
C#
maj / min
Db
F
Ab
C
Eb
G
Bb
D
min / maj
D
F
A
C
E
G
B
D
maj / min
D
F#
A
C#
E
G#
B
D#
min / maj
Eb
Gb
Bb
Db
F
Ab
C
Eb
maj / min
Eb
G
Bb
D
F
A
C
E
min / maj
E
G
B
D
F#
A
C#
E
maj / min
E
G#
B
D#
F#
A#
C#
E#
min / maj
F
Ab
C
Eb
G
Bb
D
F
maj / min
F
A
C
E
G
B
D
F#
min / maj
F#
A
C#
E
G#
B
D#
F#
maj / min
F#
A#
C#
E#
G#
B#
D#
F##
min / maj
G
Bb
D
F
A
C
E
G
maj / min
G
B
D
F#
A
C#
E
G#
min / maj
Ab
Cb
Eb
Gb
Bb
Db
F
Ab
maj / min
Ab
C
Eb
G
Bb
D
F
A
min / maj
A
C
E
G
B
D
F#
A
maj / min
A
C#
E
G#
B
D#
F#
A#
min / maj
Bb
Db
F
Ab
C
Eb
G
Bb
maj / min
Bb
D
F
A
C
E
G
B
min / maj
B
D
F#
A
C#
E
G#
B
maj / min
B
D#
F#
A#
C#
E#
G#
B#
min / maj
C
Eb
G
Bb
D
F
A
C
maj / min
C
E
G
B
D
F#
A
C#

And again the loop closes perfectly. Lots of patterns emerge and one group evolves into another. And While not the easiest to sound out on a guitar or bass though, keyboards with their sustain pedal might be a better choice to hear this coolness at first.

A 24 pitch loop. In this loop of alternating major and minor 3rd's, we get each of our 12 pitches of the chromatic scale twice (not counting the last 'C'). Thus the 24 total. Example 7.

C
E
G
B
D
F#
A
C#
E
G#
B
D#
F#
A#
Db
F
Ab
C
Eb
G
Bb
D
F
A
C
.
.
.

Easy enough yes? The symmetry of our interval loop eventually creates the perfect closure. Along the way we pick up all 12 of the major / minor key centers, now evolved from Ionian to Lydian for major and Aeolian to Dorian for minor.

So where in the music. In the fictional novel world of "Atlas Shrugged" there's a composer who writes the most profound music the world has ever known. His name is Richard Halley, and there's zero theory info about his music in the novel. The author, now perished, left no additional information of the music. No charts exist, at least that we know of. In the narrative of the story, performances of his compositions 'completely enthralled and captivated' the greatest minds of the era.

wiki ~ Atlas Shrugged
wiki ~ Ayn Rand

In every era of music there evolves a new way forward to understand our pitches and their effect on our psyche. Mr. Halley's art might have been just such a music. Somehow the fiction of this novel and my own journey crossed paths some 30 years ago, and since then I've always linked the two.

For the evolutionary effect hoped to be achieved, by anyone creating or hearing music generated in this system, would be a deeper dedication to their efforts to bring enduring peace to the world they live in.

And hats off to George Russell. Theorist, player, educator, composer and way more, George Russell's theory book, Lydian Chromatic Concept Of Tonal Organization, sets the table for my ideas to flourish. And although I've been through his work a number of times, and actually went to Boston in 2001 to try and talk in person, the following theory and system for composing, improvising and performance is not to be found in his book. Sometimes I wish it was. So while we share the same pitches, his thing is different than mine. At least as far as I can understand it, it's quite involved

So where is this #15 colortone in the music. I've never seen it or heard of it. I've asked global touring jazz artists about thee theories and been laughed at :) Their reply, "well why not have a 'b27th' ... ? Well because it makes no sense, but it sure got a good laugh at the seminar :)

There's a sharp one of course, even a #1 blue note, so I'd imagine up that up a couple of octaves we might call it sharp #15, but that's not what we're after here. Yet, I have been able to write it into an original composition or two but still neither have been publicly performed. So all in all, #15 and its potential artistic possibilities is still yet to be explored. Here's the basic arpeggio and a guitar voicing for stacking the pitches. Example 8.

Sounds polytonal. And indeed it is. Examining the first two measures of this last idea we can see the C major 7 arpeggio of measure one. Measure two has a complete D major 7th arpeggio also. The voicing of the chord to close out the line is a combination of root, major 3rd and major 7th, of each of these two major 7th chords.

The flip side. Might we flip the major 3rd / minor 3rd symmetry to minor 3rd / major 3rd and create an extended minor sounding arpeggio? Absolutely. We don't end up at sharp / #15 though. We close back on our starting pitch. Examine the pitches and their sound from our relative minor pitch A natura,l of C major. Ex. 8a.

Lovely chord huh ? Unfortunately it's not really playable on my six stringed instrument. Maybe this will be music for the seven and even eight (?) stringed guitarists? One never knows. I'll have to find a seven stringer and try it out for sure. Never thought of doing this really ... but as we often say here in Alaska ... yet another first. And there's an echo in here :)

Glimpsing a new and distant horizon. So while there's not any real call for this interval and these types of polychords in our American songbook, they do create a potentially new system of composition which harkens back to our days of polyphony, which was the rage back in Europe and probably elsewhere, during the last millennia or so.

wiki ~ polyphony

A new system of tonal organization. The curious aspect of this symmetrical arpeggiation is that each one organically evolves into a next, in a series of alternating major / minor hues. And while we have a similar situation today with our standard theory thinking and pitch groupings, the ability to arpeggiate and create various polyphonies, to modulate or move away from our chosen key center, we generally must borrow pitches of the new key center that we want to move towards. Whereas in this new system, following along the pitches of the natural, symmetrical arpeggio can unobtrusively move us from one tonal environment to another, while getting off at any pitch along the way and exploring its own mode from there. Again, similar to our diatonic realm, just a wee bit different structurally. And in the 'wee bit', there might be a new way forward for the next generation of composers.

Review ... and we're out of numbers too :( In creating a perfectly symmetrical arpeggio of an alternating major 3rd / minor 3rd, Lydian major sequence, we can arrive at a pitch which is beyond the boundaries of our initial diatonic starting point and key center. We've an arpeggio of minor 3rd / major 3rd interval symmetry, which creates a similarly identical pair of stacked 7th chords but minor and Dorian.

That our major 3rd / minor 3rd arpeggio organically morphs into our minor 3rd / major 3rd arpeggio, and vice versa, is the structural basis of this system of tonal organization for modulation, composition and improvisation.

And #15 is also the last of our numbers Amigos ... :( Though we don't bump into our starting point in this grand loop, as '16' would be sweet 'D', we know we would eventually do just that; close, and in doing so, creating that perfect closure of art / music components; in pitches, in letter names, in applying numbers, loops and groups, and progressions, in rhythms, sequences and permutations, and of the myriad of folks in our local universe, creating an unending diversity of musical art.

"Now ain't that something."

wiki ~ Jerry Garcia

Dr. Alan Frank was the professor at college who hipped me to this #15 colortone. We talked a lot about it, or he did, about where it might go as a puzzle piece of composing, and I didn't didn't have sufficient background to fully understand. But, the gist of it is here, thanks to this good Doctor ! :) We hope, Dr. Frank and I, that there's something cool here for U 2. Find it if you can.

References. References for this page's information comes from school, books and the bandstand and made way easier by the folks along the way.

References academia Alaska. And when you need university level answers to your questions and musings, and especially if you are considering a career in music and looking to continue your formal studies, begin to e-reach out to the Alaska University Music Campus communities and begin a dialogue with some of Alaska's own and finest resident maestros !

"One is not born a genius, one becomes a genius."

wiki ~ Simone de Beauvoir